By comparing with the
evolution of magnetic field strength \(B \propto \sqrt{ \mathcal {E}\rho }\) 
as a function of density numerically measured by
[1]} from simulations on magnetic field amplification during gravitational collapse,
the analytical expectation for nonlinear dynamo in a collapsing system (dashed line in Fig. REF ) agrees well with the numerical
result.
It demonstrates the importance of
reconnection diffusion and the breakdown of flux-freezing assumption.
Table REF  clearly shows the differences between the cases with reconnection diffusion and flux-freezing
for the evolution of magnetic fields during the gravitational collapse.
This result is important for studying the dynamics of magnetic fields and their effects on the primordial star formation
[2]}, [3]}.
<TABLE><FIGURE>